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arXiv · 2601.05189

Distribution of values of higher derivatives of $L'(s,\chi)/L(s,\chi)$

Samprit Ghosh
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Abstract

In this article, we study the value distribution theory for the first derivative of the logarithmic derivative of Dirichlet $L$-functions, generalizing certain results of Ihara, Matsumoto et al. related to ``$M$-functions'' for $\sigma = \operatorname{Re}(s) > 1$. We then discuss the main obstruction toward generalization to higher derivatives.

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Samprit Ghosh. 2026-01-08. Distribution of values of higher derivatives of $L'(s,\chi)/L(s,\chi)$. https://arxiv.org/abs/2601.05189

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